This invention relates to the determination of the elastic moduli and ultrasonic attenuation of materials and, more particularly, to the determination of elastic moduli and ultrasonic attenuation by sample resonant frequency excitation. This invention is the result of a contract with the Department of Energy (Contract No. W-7405-ENG-36).
The elastic properties of solid materials, described by their elastic moduli, are of great technological and scientific interest. The elastic moduli simply relate linear, reversible strains in the material to the applied (external) stresses. The elastic moduli also contain important information about the forces between individual atoms in different three-dimensional configurations, i.e., in different periodical crystal lattices and in the more or less random and disordered arrangements of atoms found in amorphous or glassy solids. The elastic moduli are basic physical parameters which give a direct link between macroscropic material properties and the atomic level structure of the material.
In the most general case, 36 independent elastic moduli are needed to fully describe the elastic stress-strain relationships in solid materials. In practice, however, different types of symmetries reduce the required number of elastic moduli considerably and, in the case of cubic single crystals, only three independent moduli are needed. Furthermore, in isotropic (non-textured) materials and amorphous solid materials, the number of independent elastic moduli is reduced by one, leaving only two elastic moduli to be determined experimentally.
The most common methods employed to determine elastic moduli are based on the measurement of sound velocities. In the standard resonance methods for measuring sound velocities, a rectangular or cylindrical sample, having one relatively large dimension, is excited for flexural, torsional, or longitudinal vibration, the mode of vibration determining the type of elastic modulus to be measured. With this method, usually only one elastic modulus is determined for each sample and measurement.
For samples other than long rods or thin reeds, i.e., samples with comparable dimensions, these simple techniques are not useful because there is no known analytical relationship that allows the elastic moduli to be deduced from the measured mechanical resonance frequencies. For some simple solid shapes, such as spheres, spherical shells, cubes and rectangular parallelepipeds, analytical methods have been developed to calculate the spectrum of mechanical resonance frequencies from a set of assumed elastic moduli. Then, a comparison of the calculated and measured spectra allows the indirect determination of the sample's elastic moduli.
A resonant sphere technique developed by Fraser and LeCraw, and described by E. Schreiber et al., "Resonant-Sphere Methods for Measuring the Velocity of Sound," Elastic Constants and Their Measurement, McGraw-Hill, 1974, is applicable only to homogeneous and isotropic materials. The three elastic constants of a cube-shaped cubic single crystal can be determined as described in H. H. Demarest, Jr., "Cube-Resonance Method to Determine the Elastic Constants of Solids," 49 J. Acoust. Soc. Amer., No. 3, Part 2, pp. 768 (1971). This technique was extended to rectangular parallelepiped samples with orthorhombic crystal symmetry and nine independent elastic constants by I. Ohno, "Free Vibration of a Rectangular Parallelepiped Crystal and Its Application to Determination of Elastic Constants of Orthorhombic Crystals," 24 J. Phys. Earth, pp. 355 (1976). In all of these resonance techniques, a sample is lightly clamped between two piezoelectric transducers for excitation and detection of the sample response. A maximum response is detected when the excitation frequency coincides with any resonant frequency of the sample.
In this rectangular parallelepiped resonance (RPR) method, the determination of elastic constants is based on the matching of theoretically calculated and experimentally measured resonance spectra. A resonance spectrum is calculated starting from the known dimensions and density of the sample and from the estimated values of a known set of elastic constants of the material forming the sample. A trial and error technique for determining the sample constants is described in U.S. Pat. No. 4,976,148, "Resonant Ultrasound Spectrometer," filed Sep. 12, 1989, incorporated herein by reference.
One problem with the RPR technique is that transducer contact with the sample can alter the detected resonance spectra and introduce harmonic resonances into the spectra. Another limitation to high-temperature measurements arises from the glues and epoxies used to hold the piezoelectric transducers in the apparatus. Another problem is that piezoelectric transducers are not operable at high temperatures and high temperature data cannot be obtained. One other problem is that samples cannot easily be removed and replaced in the clamping device with reproducible results. These and other problems in the prior art are overcome by the present invention wherein magnetostriction is employed to remotely excite a sample and detect the sample response.
Accordingly, one object of the present invention is to provide an excitation and response detection system for operating at high sample temperatures.
Another object of the present invention is to remotely excite a sample through an excitation frequency range and detect the resonant responses.
One other object is to eliminate the introduction of sample holder resonances into the sample resonance spectrum.
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.